超越亚纯函数的拟亏值

Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (6): 1474-1480.

• Articles • Previous Articles Next Articles

Valiron Quasi-Deficient of Meromorphic Functions

LIU Dan¹, DENG Bing-Mao², YANG De-Gui¹

1.Department of Mathematics, College of Science, South China Agricultural University, Guangzhou 510642;
2.South China Institute of Software Engineering, Guangzhou University, Guangzhou 510990

Received:2013-03-05 Revised:2014-05-27 Online:2014-12-25 Published:2014-12-25
Supported by:
国家自然科学基金 (11371149, 61375006) 资助

PDF (PC)

216

Abstract

Abstract:

Let f(z) be a transcendental meromorphic function, and let 0<δ< 1, if

lim—_r→∞log T(r+1/r,f )/log T(r, f)<+∞,

then there exist a_n (n=1, 2, …), such that the set {a: ?₁₎(a, f)>δ} is a subset of

∩^∞_j=1∪^∞_n=j{a:|a-a_n|<e-^enσ},

which means {a:Δ₁₎(a, f)>δ} is a set of finite μ-measure.

Key words: Meromorphic functions, Valiron quasi-deficient, μ-Measure

CLC Number:

30D35

Cite this article

LIU Dan, DENG Bing-Mao, YANG De-Gui. Valiron Quasi-Deficient of Meromorphic Functions[J].Acta mathematica scientia,Series A, 2014, 34(6): 1474-1480.

share this article

0
/ / Recommend

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://121.43.60.238/sxwlxbA/EN/

http://121.43.60.238/sxwlxbA/EN/Y2014/V34/I6/1474

Trendmd

[1] Hyllengren A. Valiron deficient values for meromorphic functions in the plane. Acta Math, 1970, 124: 1--8

[2] 杨乐. 亚纯函数的拟亏值. 数学学报, 1984, 27: 249--256

[3] Furruta M, Toda N. On exceptional value of meromorphic functions of divergence class.J Japan Math Soc, 1973, 25(4): 667--679

[4] 方明亮, 郭辉. 亚纯函数的修正Valiron拟亏值. 四川师范学院学报(自然科学版), 1992, 13(2): 111--117

[5] 杨乐. 值分布论及其新研究. 北京: 科学出版社, 1995

[6] Gol'dberg A, Ostrovskii I. Value Distribution of Meromorphic Functions. Translations of Mathematical Monographs, 236,
Providence, RI: American Mathematical Society, 2008

Related Articles 12

[1]	Zhao Lijuan. Normal Families of Meromorphic Functions and Multiple Values [J]. Acta mathematica scientia,Series A, 2015, 35(2): 256-263.
[2]	QI Xiao-Guang, YANG Lian-Zhong. Value Sharing for a Meromorphic Function with Its q-Shift Difference [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1372-1380.
[3]	WANG Xue-Qin. Normal Families and Shared Values of Meromorphic Functions [J]. Acta mathematica scientia,Series A, 2014, 34(4): 1008-1013.
[4]	LI Xiao-Min, YI Hong-Xun. UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE NONLINEAR DIFFERENTIAL POLYNOMIALS SHARE ONE VALUE OR HAVE THE SAME FIXED POINTS IN AN ANGULAR DOMAIN [J]. Acta mathematica scientia,Series A, 2014, 34(3): 593-609.
[5]	QI Xiao-Guang, LIU Yong, YANG Lian-Zhong. Nevanlinna Theory for the f(qz+c) and Its Applications [J]. Acta mathematica scientia,Series A, 2013, 33(5): 819-828.
[6]	DUAN Xi-Sheng, XIE Li. Shared Value and Normality of Families of Meromorphic Functions [J]. Acta mathematica scientia,Series A, 2013, 33(2): 242-245.
[7]	ZENG Cui-Ping, LEI Chun-Lin, YANG De-Gui. On Miranda's Normality Criterion [J]. Acta mathematica scientia,Series A, 2012, 32(4): 691-697.
[8]	ZHANG Han, XIE Dong, ZHANG Qiang-De. Normality Criterion of Meromorphic Functions Concerning Shared Set [J]. Acta mathematica scientia,Series A, 2011, 31(5): 1290-1294.
[9]	HUANG Zhi-Gang. On the Orders of Growth of Meromorphic Solutions of Certain Linear Differential Equations with Meromorphic Coefficients [J]. Acta mathematica scientia,Series A, 2010, 30(4): 1071-1079.
[10]	CHEN Jun-Fan, LIN Wei-Chuan, Chen-Sheng-Jiang. Meromorphic Functions that Share Three Weighted Values [J]. Acta mathematica scientia,Series A, 2009, 29(6): 1714-1723.
[11]	Liu Yongmin;Hu Zhangjian. Some Integral Criteria for α -Normal Functions [J]. Acta mathematica scientia,Series A, 2008, 28(3): 530-534.
[12]	Wu Guirong Pan Biao. On Common Borel Points of a Meromorphic Function and its Differential Polynomial in the Unit Circle [J]. Acta mathematica scientia,Series A, 2000, 20(4): 540-546.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 10

[1]	Wu Zhaojun, Sun Daochun. On the Borel Direction of Largest Type of Quasimeromorphic Mappings[J]. Acta mathematica scientia,Series A, 2006, 26(1): 15 -020 .
[2]	Zhang Li; Zhou Weijun. On the Global Convergence of the Hager-Zhang Conjugate Gradient Method with Armijo Line Search[J]. Acta mathematica scientia,Series A, 2008, 28(5): 840 -845 .
[3]	An Guimei\|Hou Jinchuan. Multiplication-Preserving Maps On Matrix Algebras[J]. Acta mathematica scientia,Series A, 2008, 28(6): 1194 -1205 .
[4]	Wang Chunxiang. Independence Number in Claw-free Cubic Graphs[J]. Acta mathematica scientia,Series A, 2009, 29(1): 145 -150 .
[5]	Xu Huiming;Liu Taishun. Boundary Values and Duality of Some Spaces of Holomorphic[J]. Acta mathematica scientia,Series A, 2006, 26(1): 113 -123 .
[6]	Lin Xiaoning. MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS TO SECOND ORDER SINGULAR DIFFERENTIAL SYSTEMS[J]. Acta mathematica scientia,Series A, 2006, 26(6): 1105 .
[7]	Jiang Yiwen. Cross-estimate and Tightness for Non-symmetric Markov Processes[J]. Acta mathematica scientia,Series A, 2007, 27(5): 923 -930 .
[8]	Chen Fulai ;Wen Xianzhang. Impulsive Asymptoticity for Impulsive Functional Differential Equation [J]. Acta mathematica scientia,Series A, 2006, 26(2): 287 -296 .
[9]	Zeng Linrui; Zhu Zhongyi. Variance Component Testing in Semiparametric Generalized Linear Model for Longitudinal Data[J]. Acta mathematica scientia,Series A, 2008, 28(4): 585 -594 .
[10]	BAI Ding-Yong, MA Ru-Yun. The Existence of Positive Solutions for a Singular Boundary Value Problem with p Laplacian Operator[J]. Acta mathematica scientia,Series A, 2005, 25(2): 166 -170 .

Abstract
References
Related Articles
Metrics
Comments
Recommended

TOP